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Mirror Symmetry and Discriminants

Publication ,  Journal Article
Aspinwall, PS; Plesser, MR; Wang, K
February 15, 2017

We analyze the locus, together with multiplicities, of "bad" conformal field theories in the compactified moduli space of N=(2,2) superconformal field theories in the context of the generalization of the Batyrev mirror construction using the gauged linear sigma-model. We find this discriminant of singular theories is described beautifully by the GKZ "A-determinant" but only if we use a noncompact toric Calabi-Yau variety on the A-model side and logarithmic coordinates on the B-model side. The two are related by "local" mirror symmetry. The corresponding statement for the compact case requires changing multiplicities in the GKZ determinant. We then describe a natural structure for monodromies around components of this discriminant in terms of spherical functors. This can be considered a categorification of the GKZ A-determinant. Each component of the discriminant is naturally associated with a category of massless D-branes.

Duke Scholars

Publication Date

February 15, 2017
 

Citation

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Aspinwall, P. S., Plesser, M. R., & Wang, K. (2017). Mirror Symmetry and Discriminants.
Aspinwall, Paul S., M Ronen Plesser, and Kangkang Wang. “Mirror Symmetry and Discriminants,” February 15, 2017.
Aspinwall PS, Plesser MR, Wang K. Mirror Symmetry and Discriminants. 2017 Feb 15;
Aspinwall, Paul S., et al. Mirror Symmetry and Discriminants. Feb. 2017.
Aspinwall PS, Plesser MR, Wang K. Mirror Symmetry and Discriminants. 2017 Feb 15;

Publication Date

February 15, 2017